Transliteration is the conversion of a text from one script to another.
For instance, a Latin transliteration of the Greek phrase "Ελληνική Δημοκρατία", usually translated as 'Hellenic Republic', is "Ellēnikḗ Dēmokratía".
Transliteration is not concerned with representing the sounds of the original, only the characters, ideally accurately and unambiguously. Thus, in the above example, λλ is transliterated as 'll', but pronounced /l/; Δ is transliterated as 'D', but pronounced 'ð'; and η is transliterated as 'ē', though it is pronounced /i/ (exactly like ι) and is not long.
Conversely, transcription notes the sounds but not necessarily the spelling. So "Ελληνική Δημοκρατία" could be transcribed as "elinikí ðimokratía", which does not specify which of the /i/ sounds are written as η and which as ι.
Systematic transliteration is a mapping from one system of writing into another, typically grapheme to grapheme. Most transliteration systems are one-to-one, so a reader who knows the system can reconstruct the original spelling.
Transliteration is opposed to transcription, which maps the sounds of one language into a writing system. Still, most systems of transliteration map the letters of the source script to letters pronounced similarly in the target script, for some specific pair of source and target language. If the relations between letters and sounds are similar in both languages, a transliteration may be very close to a transcription. In practice, there are some mixed transliteration/transcription systems that transliterate a part of the original script and transcribe the rest.
For many script pairs, there is one or more standard transliteration systems. However, unsystematic transliteration is common.
In Modern Greek (and since the Roman Imperial period), the letters <η> <ι> <υ> and the letter combinations <ει> <oι> <υι> are pronounced [i] (except when pronounced as semivowels), and a modern transcription renders them all as <i>; but a transliteration distinguishes them, for example by transliterating to <ē> <i> <y> and <ei> <oi> <yi>. (As the ancient pronunciation of <η> was [ɛː], it is often transliterated as an <e> with a macron, even for modern texts.) On the other hand, <ευ> is sometimes pronounced [ev] and sometimes [ef], depending on the following sound. A transcription distinguishes them, but this is no requirement for a transliteration. The initial letter 'h' reflecting the historical rough breathing in words such as Ellēnikē should logically be omitted in transcription from Koine Greek on, and from transliteration from 1982 on, but it is nonetheless frequently encountered.